It would definitely be nice to be able to work with a partial Category
class, where for example the objects could be constrained to belong to a
class. One could then restrict a Category to a type level representation
of the natural numbers or any other desired set. Kind polymorphism should
make this easy to define, but I still don't have a good feel for whether it
is worth the complexity.
On Dec 21, 2012 6:37 AM, "Tillmann Rendel"
Hi,
Christopher Howard wrote:
instance Category ...
The Category class is rather restricted:
Restriction 1: You cannot choose what the objects of the category are. Instead, the objects are always "all Haskell types". You cannot choose anything at all about the objects.
Restriction 2: You cannot freely choose what the morphisms of the category are. Instead, the morphisms are always Haskell values. (To some degree, you can choose *which* values you want to use).
These restrictions disallow many categories. For example, the category where the objects are natural numbers and there is a morphism from m to n if m is greater than or equal to n cannot be expressed directly: Natural numbers are not Haskell types; and "is bigger than or equal to" is not a Haskell value.
Tillmann
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